Domain partitioning as a result of deformation in the framework of large-strain Cosserat plasticity

TL;DR

This paper analytically investigates domain partitioning and micro-rotation patterning in large-strain Cosserat plasticity, revealing mechanisms for grain formation in deformed solids.

Contribution

It provides explicit solutions for a shear problem in Cosserat plasticity, linking micro-rotation patterns to domain partitioning and grain formation.

Findings

Patterning arises for certain parameters.

Domain partitions into regions with constant rotations.

Micro-rotations follow an Allen-Cahn type equation.

Abstract

In the framework of the rate-independent large-strain Cosserat theory of plasticity we calculate analytically explicit solutions of a two-dimensional shear problem. We discuss two cases where the micro-rotations are stationary solutions of an Allen-Cahn equation. Thus, for a certain parameter range, patterning arises and the domain is partitioned into subsets with approximate constant rotations. This describes a possible mechanism for the formation of grains and subgrains in deformed solids.